MorganS - Thank you! I didn't realize the Arduino could recognize two inputs at the same time, for some reason I thought it just checked one at a time very quickly. I was able to restructure my code to do exactly what I wanted.
void loop() {
if((digitalRead(buttonPin02) == HIGH)&&(digitalRead(buttonPin01) == HIGH))
{
Serial.print(3);
Serial.flush();
delay(20);
}
else if(digitalRead(buttonPin01) == HIGH)
{
Serial.print(1);
Serial.flush();
delay(20);
}
else if(digitalRead(buttonPin02) == HIGH)
{
Serial.print(2);
Serial.flush();
delay(20);
}
}